Bends for circular wave guides



Aug. 30, 1960 a. R. P. MARIE BENDS FOR CIRCULAR WAVE GUIDES Filed Dec.5, 1958 2 Sheets-Sheet 1 iiI/IIIIII/IIIA a,

EXM'HNER Aug. 30, 1960 G. R. P. MARIE szmas FOR CIRCULAR wm: cums 2Sheets-Sheet 2 Filed Dec. 3, 1958 United States Patent BENDS FORCIRCULAR WAVE GUIDES Georges Robert Pierre Mari, 16 Rue de Varize,Paris, France Filed Dec. 3, 1958, Ser. No. 777,874 Claims priority,application France Dec. 19, 1957 Claims. (Cl. 333-98) This inventionrelates to bends for circular wave guides, and more particularly tobends for circular wave guides for the propagation of TE, modeelectromagnetic waves.

The bends according to the invention preferably consist of metalelements in the form of rectangular toroidal segments. The elements arein the shape of a wedge in cross-section substantially square and willhereinafter be referred to as segmental metal elements. The bendscomprise: segmental metal elements having two converging plane surfacesforming a first angle between them and pierced with a circular apertureforming a section of the guide; dielectric prisms introduced between twosegmental metal elements and having plane surfaces forming between thema second angle; and means for securing a number of such elements andprisms relatively to one another.

However, while the just described arrangement is a preferred form ofembodiment of the invention, it must be understood that said prismsmight as well be mounted inside ordinary bent wave guide tubing, as themain advantage of said arrangement is greater facility for securing saidprisms inside said guide. The main original feature of the invention isa new method of construction of said prisms.

In the device of the invention, the angle of said prisms is withouteffect on the direction of wave propagation and is, for instance, equalto the angle between the surfaces of a segmental metal element, whilethe apparent permittivity and therefore the apparent refractive index ofeach prism vary from place to place therein in such manner that thephase wave length in the bend at any part thereof is proportional to theradius of the bend at such part. This is effected by providing the planesurfaces of said prisms with grooves of suitable size, shape andarrangement.

The invention will hereinafter be described in detail with reference tothe accompanying drawings wherein:

Figure 1 is a perspective view of a segmental metal element;

Figures 2 and 3 are a view in longitudinal section and a view incross-section, respectively, of a preferred embodiment of the invention,and

Figures 4 and 5 are explanatory diagrams of the construction of the bendillustrated in Figures 2 and 3.

Figure 1 illustrates a segmental metal element 1 of a bend of a circularwave guide. The element 1 is in the shape of a prism or wedge withoutany edge. The plane surfaces 2, 3 converge along an imaginary edge 25 ata reduced angle 3, for instance, of the order of 5 or less. Each element1 is pierced with a circular aperture 4, the axis 5 of which isperpendicular to the plane 6 bisecting the dihedron formed by thesurfaces 2, 3. When a number of said elements are stacked to form thebend, the internal wall of the guide is formed by the inner walls of theapertures 4 of consecutive elements.

The four corners of the element 1 are pierced with transverse apertures7, 8, 7', 8' which extend parallel with the axis 5 and which are adaptedto receive arcuate metal rods such as 10, 11. The elements 1 are clampedon the rods 10, 11 by clamping screws 9, and against one another by nuts12, which bear against flanges 13 of straight sections 14 of thewaveguide at each end of the bend. The method of securing the prismsbetween the metal elements will be explained later on, in connectionwith Fig. 2.

It has been found that if a stack of metal and dielectric elementsaccording to the invention is used to produce a deflection ofelectromagnetic waves, the TE mode is maintained satisfactorily and witha very reduced power loss, even with a bend having a much shortercurvature radius than in known systems.

Such loss is mainly caused by parasitic waves produced by reflections onthe surfaces of the prisms 20 within the bend. The power associated withthese higher modes is radiated outside the waveguide, for the highermodes are associated with longitudinal currents which can travel out ofthe bend in the dielectric-filled spaces between the segmental metalelements.

In the embodiment of a bend illustrated in Figures 1 and 2, to obviatereflections at transitions from a dielectric surface to the air, theapparent refractive index of the dielectric prisms varies with thedistance from a point on the prism to the axis of the annulus.

To explain the construction of the novel dielectric prisms, it will benoted with reference to Figure 4 that, in a medium consisting ofdielectric plates 44 which are of thickness a and which have parallelsurfaces and which are disposed parallel with one another and spacedapart by a distance b between the central planes of two consecutiveplates, the apparent permittivity e' of such medium is related to thepermittivity e of the dielectric substance forming the plates by theformula:

for a plane wave which travels in a direction 40 parallel with the planeof the plates 44, has its electric field parallel therewith and is of awavelength considerably greater than 2b.

Referring to Figures 2 and 3, three segmental metal elements 27, 28 and29 similar to those illustrated in Figure 1 are assembled by means ofrods 30 which extend through apertures 31 and are provided with clampingnuts 32. Two variable-refractive-index dielectric prisms 33 and 34 havean apex angle equal to the apex angle of the segmental metal elements.In Figure 2, the prisms 33 and 34 are shown as being slightly spacedapart but when the nuts 32 are tightened they engage by way of theirsurfaces 48 and 48'. The prisms 33 and 34 are formed with grooves 35, 36and 37 of a shape to be described hereinafter, annular cylindricalprojections 41 to 43 being left therebetween. The grooves are of a depthsuch that a solid wall 49 is left in the plane bisecting each prism. Forthe sake of simplicity, only three such grooves and projections areshown in Figures 2 and 3 but in practice more can be provided. Theperiphery of each prism is formed by a thin plate 38 engageable betweentwo consecutive segmental metal elements. The rods 30 extend throughapertures 39 in the fixing plates 38.

The prisms 33 and 34 are made, for instance, of moulded polyethylene.

The grooves 35 to 37 and the cylindrical projections 41 to 43 have ageneral substantially circular shape but in actual fact their shape iscomplex, since their thicknesses vary and the bounding lateral walls arenot coaxial.

The construction of the annular grooves and projections will beexplained with reference to Figure 5.

Let be the center of the thin wall 49 and coincident with the centers ofthe circular apertures pierced in the elements 27 and 28. The wall 49 issituated in a plane passing through the axis of revolution of theannulus, a part of which forms the bend according to the invention.

Let Or and 0y be two reference axes taken in the plane of the wall 49.The axis Ox is perpendicular to the axis of the annulus. The axis Oyperpendicular to Ox is parallel with the axis of the annulus. A thirdaxis Oz is perpendicular to the cross-section of the bent circularguide--i.e. tangential to the center line 45 of the bend (Figure 2)--andforms a trirectangular trihedron with the axes Ox and Oy.

The axis Ox is the common axis of symmetry of all the grooves 35 to 37and projections 41 to 43.

Let:

N=the number of annular projections or rings in the D=the diameter ofthe circular guide;

R=the radius of curvature of the bend-Le. the radius of the circleformed by the center line 45.

The annular projection of order k (the ring of order unity is thesmallest diameter ring) is included between two cylinders of radius (R-p/2) and (R +p/2), the axes of revolution of which meet the axis Ox atabscissae points .7c=e, and x: -e respectively.

R: will be called the mean radius" of the ring of order k.

p will be called the mean thickness" of the rings and is independent ofk.

The mean radius of the ring is found from the formula:

In Figure 5, a circle 46 of center 0 and radius R =D/4 N is the meancircle of the ring 41, while circles 47 and 47' have centers 0 and 0,respectively and radii R -p/2 and R,+p/2 respectively. The points 0 andO: are on the x axis and have as abscissae e and e respectively.

If the quantity e is small as compared with the guide diameter D, thethickness of the ring of order k in de pendence upon the azimuth(calculated in the plane xOy and taking Ox as the axis of origin) isfound from the formula:

pt()= t cos Since cos =x/R Formula 3 can be written:

ek i

It will therefore be apparent that the various rings form a mediumsimilar to that of Figure 4, except that the plates 26 are replaced byannular cylindrical plates 41 to 43, a is replaced by p and b isreplaced by (R -1K =D/2N Formula 1 applied to rings of the prism 33gives:

4 revolution of the annulus of which the bend forms a part. Hence:

If the bend radius R is fairly large relative to the wave guide diameterD, only the first x/R term of Formula 7 is required.

By identifying the second members of Formulae 5 and 7, the latter beingreduced to the first x/R order, there As a rule, the diameter D ispredetermined; the radius R is made fairly large to exclude non-linearx/R terms.

Advantagcously, to reduce losses in the dielectric of the rings 41 to 43the same are extremely thin. The least thickness is that of the Nth ringon the x axis. Let this thickness be denoted by p It is equal, accordingto Formula 3, to:

Of course, this minimum value must be compatible with mouldingrequirements, and Formula 8 combined with Formula 9 appears as afirst-order equation in p, giving:

Once p is known, e and more generally a quantities can be calculatedfrom the formula:

so that all the parameters of the moulded dielectric prism according tothe invention are provided.

To prevent parasitic reflections of the kind already mentioned, theprismatic shape of the dielectric system illustrated in Figures 2 and 3is such that the boundary planes 48 and 48 of two consecutive prisms 33and 34 are contiguous; in other words, the rings of the same meandiameter of two consecutive systems engage with one another.

In conclusion, a calculation example will be given for the simple caseof a bend for a circular waveguide having a diameter D of 7 cm. andserving for the propagation of electromagnetic waves of a frequency of10,000 mc./ s. A =3 cm.). The bend radius R is 70 cm.

The moulded polyethylene prismatic member of permittivity e=2.6comprises three rings; the distance between the rings is much less thanone half-wavelength and so there is no likelihood of parasitic modesbeing produced.

In order that the prismatic member may be readily moulded, the thicknessp of the third ring on the x axis is 0.5 mm.

The mean thickness of each of the three rings is p=l mm. Theeccentricities of the ring-bounding cylinders are found from Formula 11to be:

The mean radii of the rings corresponding to these three eccentricitiesare:

What is claimed is:

1. A low loss bend for a circular wave guide propagating a 'I'E wave,comprising a length of circular crosssection metallic wave guide theaxis of which is bent with a given radius and a plurality ofwedge-shaped prisms of dielectric material mounted inside said guidelength and having two converging plane faces substantially perpendicularto said bent axis, wherein at least part of said prisms have theirconverging plane faces provided with grooves of progressively varyingwidth and depth from the inside towards the outside of said bend, saidgrooves provided on said faces being so shaped as to permit said TE waveto propagate around said bend with no substantial distortion.

2. A bend as claimed in claim 1, wherein the widths and depths of saidgrooves progressively vary in such a manner that the phase wave lengthin said bend at any part thereof be proportional to the radius of saidbend in latter said part.

3. A bend as claimed in claim 1, wherein said grooves are limited bynon-concentric circular cylindrical surfaces substantially parallel tosaid axis and the radii of which progressively increase from said axistowards the inside surface of said guide.

4. A bend as claimed in claim 1, wherein said guide length is made ofspaced metal elements having the shape of rectangular toroidal segmentsand having two converging plane faces which form an angle, each one ofsaid elements being provided with a circular aperture.

5. A bend as claimed in claim 4, wherein spacings are provided betweensaid metal elements and wherein said prisms are secured to said guidelength by means of projections provided in said prisms and tightly heldin said spacings between said elements.

References Cited in the file of this patent UNITED STATES PATENTS2,129,712 Southworth Sept. 13, 1938 2,596,251 Kock May 13, 19522,779,006 Albersheim Jan. 22, 1957 2,785,397 Rust et a1. Mar. 12, 1957OTHER REFERENCES Steutzer: Proceedings of the IRE, Sept. 1950, vol. 38,No. 9, pages 1053-1056.

